Fix error - win test still using choco not pymanager

Author: AlenkaF

ci/docker/python-wheel-windows-test-vs2022.dockerfile

@@ -28,6 +28,11 @@ FROM ${base}
 
 # Define the full version number otherwise choco falls back to patch number 0 (3.10 => 3.10.0)
 ARG python=3.10
+RUN (if "%python%"=="3.10" setx PYTHON_VERSION "3.10.11" && setx PYTHON_CMD "py -3.10") & \
+    (if "%python%"=="3.11" setx PYTHON_VERSION "3.11.9" && setx PYTHON_CMD "py -3.11") & \
+    (if "%python%"=="3.12" setx PYTHON_VERSION "3.12.10" && setx PYTHON_CMD "py -3.12") & \
+    (if "%python%"=="3.13" setx PYTHON_VERSION "3.13.7" && setx PYTHON_CMD "py -3.13") & \
+    (if "%python%"=="3.14" setx PYTHON_VERSION "3.14.0" && setx PYTHON_CMD "py -3.14")
 
 # hadolint ignore=DL3059
 RUN choco install -r -y --pre --no-progress --force python --version=%PYTHON_VERSION%
@@ -37,4 +42,4 @@ RUN %PYTHON_CMD% -m pip install -U pip setuptools
 COPY python/requirements-wheel-test.txt C:/arrow/python/
 RUN %PYTHON_CMD% -m pip install -r C:/arrow/python/requirements-wheel-test.txt
 
-ENV PYTHON=$python
+ENV PYTHON=${python}